How to Calculate 2 1/3 - 1 7/8 3/4: Step-by-Step Guide for Beginners

This guide will help you understand the process of subtracting mixed numbers with fractions. By following the steps below, you can effectively perform the calculation 2 1/3 - 1 7/8 3/4.

Step 1: Convert Mixed Numbers to Fractions

First, we need to convert the mixed numbers to improper fractions by multiplying the whole number by the denominator, adding the numerator, and placing the result over the original denominator.

2 1/3 (2 × 3) 1 7/3

1 7/8 (1 × 8) 7 15/8

1 3/4 (1 × 4) 3 7/4

The equation becomes: 7/3 - 15/8 - 7/4

Step 2: Find the Least Common Denominator (LCD)

Next, find the least common denominator of the fractions. The denominators here are 3, 8, and 4. The least common multiple (LCM) of these numbers is 24.

Step 3: Convert Each Fraction to Have a Common Denominator

7/3 (7 × 8)/(3 × 8) 56/24

15/8 (15 × 3)/(8 × 3) 45/24

7/4 (7 × 6)/(4 × 6) 42/24

The equation now looks like this: 56/24 - 45/24 - 42/24

Step 4: Perform the Subtraction

Now, perform the subtraction using the common denominator.

56/24 - 45/24 (56 - 45)/24 11/24

11/24 - 42/24 (11 - 42)/24 -31/24 29/24 (since -31/24 simplifies to 29/24 and -31 24 -7, and -7/24 is not a proper fraction, 29/24 is simplified)

The final answer is 29/24, which can also be written as 1 5/24 (since 29/24 24/24 5/24 1 5/24).

Alternative Methods

Here are a few alternative ways to perform the calculation:

Method 1: Adjusting Fractions

Convert each fraction to have a common denominator of 24:

2 1/3 28/24

1 7/8 21/24

1 3/4 18/24

Subtract the fractions: 28/24 - 21/24 - 18/24 56/24 - 45/24 11/24

Method 2: Least Common Multiple (LCM) Adjustment

Convert to improper fractions with a common denominator of 96:

2 1/3 7/3 224/96

1 7/8 15/8 180/96

1 3/4 7/4 168/96

Subtract the fractions: 224/96 - 180/96 - 168/96 12/96 1/8

Conclusion

By following the steps provided and trying different methods, you can easily calculate the result of the operation 2 1/3 - 1 7/8 3/4. The final answer is 29/24 or 1 5/24.

Frequently Asked Questions (FAQ)

1. What is a common denominator?

A common denominator is a common multiple of the denominators of two or more fractions. It is used to add, subtract, or compare fractions with different denominators.

2. How do you find the least common denominator (LCD)?

To find the LCD, you can use the least common multiple (LCM) of the denominators or simply multiply the denominators together (though this may not always yield the least common denominator).

3. Why is it important to convert mixed numbers to improper fractions?

Converting mixed numbers to improper fractions makes it easier to add, subtract, multiply, or divide fractions. It eliminates the need for dealing with both the whole and fractional parts separately.